Tension members such as ropes and cables are subject to oscillations. These members can be excited by external forces such as wind. If the frequency of exciting forces matches the natural frequency of the tension member, then the tension member will resonate.
High velocity winds cause buildings to sway back and forth. The frequency of the building sway can match the natural frequency of the elevator causing resonance. In resonance, the amplitude of the oscillations increases unless limited by some form of dampening. This resonance can cause significant damage to both the elevator system and the structure.